Diagnostics Of Asynchronous Motors Based On Spectra Analysis Of ...

Diagnostics Of Asynchronous Motors Based On Spectra
Analysis Of Power Consumption
Mamchur Dmytro, Kremenchuk Mykhaylo Ostrogradskiy State Polytechnical University
(01.09.2004, doc. Kalinov Andrii, Kremenchuk Mykhaylo Ostrogradskiy State Polytechnical University)
Kalinov Andrii, Kremenchuk Mykhaylo Ostrogradskiy State Polytechnical University
(01.07.2002, prof. Rodkin Dmitriy, Kremenchuk Mykhaylo Ostrogradskiy State Polytechnical University)
Abstract
In paper the problem of an induction motor
operational modes evaluation with the purpose of
maintenance optimal for electric power costs
economies and electric drive system resource
magnification is considered. This analysis is suggest
to realize on the ground of both known and
formulated energy conversion quality indicators.
1. Introduction
In modern conditions of increase of requirements
to efficiency of using power resources, there is a task
of timely diagnostics of engendered defects in the
asynchronous drive systems at the enterprises, as the
most mass user (consumer).
Existing regulated methods of asynchronous
drive diagnostics need withdrawal and partial
disassembly of equipment. This will make delays in
work, and not ensure reliability at turnaround time.
The most modern methods are on-line condition
monitoring using electrical signature analysis and
vibration monitoring. These methods do not require
delays in work, and allow defining most common
defects. Analysis of operating modes allows
formulating recommendations for possibility and
efficiency evaluation of using electric drive systems
at straight-line operating conditions. It allows making
following operations, based on analysis of electric
drive system energetic parameters:
– to make diagnostics – define defects or
damages of electric drive system elements;
– to make prognosis of asynchronous motor
system remaining life basing on analysis of heat
emission in windings;
– to calculate insulation and bearings remaining
life time basing on vibration analysis;
– to estimate quality of technology operations
basing on analysis of variable components level of
instantaneous power and moment;
– to make correction of electromechanical system
operation modes by compensation of instantaneous
power variable components and optimization of
power consumption modes.
XI International PhD Workshop
OWD’2009, 17–20 October 2009
434
2. Concept
Well-known systems of electromechanical system
conditions and availability estimation are base on
vibration and current spectra analysis. They are used
for determination of equipment overall technical
conditions, defining concrete defects and observing
its progress. However, in using such systems, there
are some difficulties with separation of noise and
neighboring equipment action. Also, there is no
possibility to prognosis of system remaining life
time. Complex analysis of instantaneous currents and
voltages, and also power consumption spectra and
electromechanical system energy characteristics
(according to algorithm in [8]) allows disposing of
shortcomings of well-known systems. Three-phase
asynchronous drive power consumption or
electromagnetic moment spectra, in contrast to
currents spectra or currents envelope, allow not only
to define availability of damages and defects, but also
to estimate damage rate by power of adequate
harmonics. Using power consumption or
electromagnetic torque spectra allow to estimate
energetic component of damage and link it with
additional failure of electromechanical converter
components because of heating and vibrations.
Besides diagnostics, it allows to estimate degradation
of asynchronous motor energy efficiency. Spectra
analysis of mentioned signals allows estimating work
of electromechanical converters with substantial
non-linearity, i.e. when it is not correct to use
superposition principle [9], especially when power
supply has substantial unsinusoidality, and using
currents as diagnostic parameters leads to incorrect
analysis.
It was proposed to make estimation of
electromechanical converter operating quality and
technical state, according to [10-12], by analysis of
instantaneous power, using energy conversion quality
indicators (ECQIs). Analysis [13, 14] shows, that it is
hard to formulate valid conclusion about current
technical conditions of AD and formulate
recommendations for its use in technological
process, also to make prognosis of its workability by

formulated ECQIs. Thus, there is necessity of
increasing existing ECQIs for possibility, basing on
it, diagnostics and analysis of AD operation modes.
It may be done by using analysis of power
consumption spectra.
3. Implementation
3.1 Science objective
Development of asynchronous drives defects
detecting method based on analysis of power
consumption spectra.
3.2 Experimental results
Deterioration of asynchronous motor operation
modes appears because of electrical or mechanical
damages, or bad supply (asymmetry, unsinusoidality).
Electrical damages are caused by windings, AD's
nonlinearity, AD's parametric asymmetry, static and
dynamic unbalance. Mechanical damages are caused
by physical damages, rotor bending, bearings
slumping, bad mounting. For influence analysis of
different kinds of damages and unsoundness of
energy conversion process, the following three-phase
mathematical models of AD were developed and
investigated [15]:
- idealized motor fed with poor voltage;
- motor with improper mounting [16];
- motor with static, dynamic and combined rotor
misbalance [17];
- motor with stator winding asymmetry;
- motor with rotor winding bar break [18];
- motor with stator winding short-circuits.
Using these models for AD 4АХБ2Г100L4 (4
kilowatt; 8.7 А; 1420 rpm) running-in, idling and
different loading operations were calculated.
Operation modes were analyzed by three-phase and
each phase power spectra (fig. 1 – 7), where different
harmonics are individual for different damages [19].
Whereas some kinds of damages can become
apparent by subharmonics [20], which are symmetric
relatively to main harmonic [19], three-phase power
spectrum was separated to such zones for analysis:
– 0–5 Hz – zone of constant component;
– 6–45 Hz – zone of low-frequency component;
– 46–55 Hz – zone of power supply main
frequency;
– 56–95 Hz – contiguous zone of power supply
main frequency and double frequency;
– 96–105 Hz – zone of double power supply
main frequency.
By analogy: 106–195 Hz, 206–295 Hz, >306 Hz
– contiguous zones; 196–205 Hz, 296–305 Hz, 396–
405 Hz, 496–505 Hz, 596–605 Hz – zones of
multiply main frequency. For estimation of different
frequencies harmonics contribution to integral value
of hi-harmonics, the following quotient was used:
K
harm(
N1÷
N2
)
=
N2
2
∑Pk
1
k1=
N1
N −1
2
∑ Pk
k=
1
where N – total amount of spectra harmonics, N1,
N2 – initial and final harmonics values.
,
435
Additional analysis was carried out by ECQIs,
formulated in previous researches[10-12]. The
following factors were chosen among them:
– the factor of the energy consumption efficiency:
ε – the generalized factor describing low-quality
p
conversion integrally, ε pi – the factor describing
low-quality energy conversion specified by phase,
here i – number of phase;
– the factor, characterizing inequality of heat
generation in the stator windings, K npτ
;
– the reciprocal factor of low-quality torque
conversion Krec t = 1/
Klq
t – describing percent of
hi-harmonics in torque spectra;
– the factor of the vibration characteristics
deterioration Klq v .
Considerable torque variable component is
usually created by serious damages. That's why it is
necessary to make additional analysis to detect its
source. Analysis of experimental data [7] shows, that
operation of electromechanical systems, where
torque variable component is greater than 15% of
nominal value, results in an intensive resource
decreasing and such modes are undesirable. Limiting
values of torque variable component must be
determined subject to engine power and system
operation modes. To account these facts, quotient of
electromagnetic torque hi-harmonics is proposed:
N
∑ −
1
Kt hh = Mν
Klim
Mn
,
ν = 1
where K lim – maximum permissible value of
torque variable component comparatively to torque
nominal value, M n – nominal value of torque. When
this quotient is greater than one, such regimes are
damaging for machines. In ideal, electromagnetic
moment signal has no hi-harmonics, and quotient is
zero.
For estimation of total machine asymmetry
caused by both bad voltage and machine low-quality,
weighted average quotients for amplitudes and
phases of instantaneous power were proposed:
Pavg i = Piν
( Pav
+ Pbv
+ Pcv
) ;
ν
ϕavg i = ϕiν
( ϕav
+ ( ϕbv
+ 2π / 3)
+ ( ϕc
v + 4π
/ 3))
ν
– ratio of one-phase harmonic or phase value to
total three-phase harmonic or phase value of same
rank. Ideally, quotient is 1/3 by each of three phases
[5]. Well-behaved analysis is whenν = 2 , because
this harmonic is always present in signal with
different kinds of low-quality.
When diagnostics in real work conditions with
real power network is made, reduction to supply
from ideal power network must be done [21], or
electric energy quality indicators (EEQI) must be
taken into account [22]. For this, indicators of
voltage asymmetry ε 2 , indicator of current
asymmetry ε I 2,
indicator of power asymmetry ε P2 ,
k , indicator
indicator of voltage unsinusoidality us U
of current unsinusoidality us I
2
k were calculated.

Variation of ECQIs, when used different load or
technological process conditions, are information
attributes when estimation of asynchronous motor
system working modes is performed. However,
values of these quotients must not be rigidly
referenced with value of load, because diagnostic
operation is carried out under no-load conditions or
with unknown or stochastic changing load.
Analyzing whole quotients and power spectra, the
following conclusions can be made.
In three-phase power spectra of non-damaged
motor there is just negligible value of low-frequent
component stipulated by mathematical convertion
errors when mathematical models were calculated. In
phase power spectra there is main component of
double voltage frequency ( 2 fv
=100 Hz), and
negligible subharmonics of double voltage frequency
and single voltage frequency ( f v =50 Hz) (fig. 1, b),
which is also stipulated by mathematical convertion
errors. Main percent of high harmonics is in range of
6–45 Hz (fig. 1, a). As motor is without damages, so
quotients have limited values for ideal machine. So,
if there is just negligible low-frequent component in
spectra of three-phase power and formulated
quotients are maximally near optimal values, that
examined motor is good.
a) b)
Fig.1 Three-phase (a) and phase A (b) instantaneous power
spectra of idealized motor without damages with ideal supply.
436
K τ = 1 for all phases, it means unsinusoidality
np ( i )
of power supply. When harmonic of frequency 4 f v
is significant, it means that power supply system is
also asymmetric.
(
a) b)
c)
Fig. 2 Three-phase power spectra with non-sinusoidal
supply: a) 1, 3 harmonics; b) 1,3,5 harmonics; c) 1,3,5
harmonics, non-symmetry of amplitudes of 5-th harmonics by
phases.
( K
So, if the following rule is correct:
> 0 ) ∧(
K = K = K
ε 2
npτ
(A) npτ
(B) npτ
(C)
∧ ( ε > 0,
9)
∧(
ε
P
t hh
PA
> 0,02) ∧(
P
≈ ε
avg А2
PB
= P
≈ ε
avg B2
) ∧
= P
≈ 1)
avg C 2
= 0,
33)
∧ ( Kharm(296
- 305) ≈ 1)
= 1,
that examined motor is good, but power supply is
symmetric and non-sinusoidal, and if the following
rule is correct:
( > 0 ) ∧(
K = K = K ≈ 1)
∧ ( ε > 0,
9)
∧(
ε
p
pA
pB
PС
ε 2
npτ
(A) npτ
(B) npτ
(C)
≠ ε
≠ ε
pС
) ∧ ( K
t hh
> 0,02 ) ∧
Thus, if the following rule is correct:
( ε 2 = 0 ) ∧ ( ε p2
= 0 ) ∧ ( Knpτ
(A) = Knpτ
(B) =
= K npτ
(C) = 1)
∧ ( ε p ≈ 1)
∧ ( ε pA = ε pB = ε pС )
∧ ( Pavg
А ≠ Pavg
B ≠ Pavg
C ) ∧(
Kharm(296-
305) ≈ 1)
2
2
2
3
∧ ( Kharm(196-
205) > Kharm(146-195)
⋅10
) = 1,
that examined motor is supplied by asymmetric nonsinusoidal
system.
∧ ( Krec
t ≈ 1)
∧ ( Kt
hh < 0,
05 ) ∧
( Pavg
А = Pavg
B = Pavg
C = 0,
33)
∧
2
2
2
( Kharm(6
- 45) > 0,
75 ) = 1,
that examined motor is good, and it has ideal supply.
When there is unsinusoidality of supply system
(3-rd harmonic), appears harmonic with frequency of
6 f v (fig. 2, a) in three-phase power spectra. When
there are 3-rd and 5-th harmonics of power supply,
in spectra of three-phase power spectra appears
subharmonics of 6 f v harmonic (fig. 2, b). When
there are both unsinusoidality and asymmetry of
power supply, appears harmonics of all frequencies,
which are multiple of double power supply
frequency (fig. 2, c). Herewith, harmonics specific
for motor without damages, are constant by values
of frequency and amplitude. Main percent of high
harmonics, when there is unsinusoidality of power
supply, is in frequency of 6 f v (fig. 2). When there is
To simplify logical expressions, it is appropriate
to previously transform analyzed signals to signals,
which are received with ideal power supply [21]. In
this case, indicators ε 2 , k us U will always be zero,
and it is not necessary to take them into account
when rules are composing.
When mounting is bad, there is only low
frequency three-phase power spectra harmonics
(fig. 3, a) conditioned by low-frequent motor
vibrations. In phases power spectra there is main
harmonic with double voltage frequency and
subharmonics of single and double voltage frequency
(fig. 3, b). When mounting is worse, frequencies of
subharmonics changes, and their amplitudes grow.
Formulated indicators changes are negligible (1–2%).
This effect can be explained by approaching to
hunting frequency whith different quality of
mounting. Main percent of high harmonics is in
range of 6–45 Hz (fig. 3, a). Thus, if there is
significant low-frequent component in three-phase
asymmetry, harmonics of frequency 4 f v become
significant (fig. 2, c). Thus, if in three-phase power
power spectra and growth of indicator K t hh with
mounting degradation, with almost optimal other
spectrum there is harmonic of frequency 6 f v , and indicators, that motor has bad mounting.

( K
a) b)
Fig. 3 Three-phase (a) and phase A (b) spectra of motor
with bad mounting.
So, if the following rule is correct:
npτ
(A)
∧ ( P
avg А2
= K
= P
npτ
(B)
avg B2
= K
= P
npτ
(C)
avg C 2
= 1)
∧ ( K
= 0,
33)
∧
t hh
> 0,
02)
∧
∧ ( ε pA = ε pB = ε pС ) ∧ ( K harm(6-
45) > 0,
75)
= 1,
that examined motor is badly mounted.
When rotor is dynamic or static misbalanced,
there is harmonic in three-phase power spectra,
which relates to rotation frequency. Thus, when noload,
there is harmonic with frequency 100p in threephase
power spectra (here p – number of ports). So,
if there is significant component with rotation
frequency in three-phase power spectra, and
weighted average quotients are not equivalent by
phases, that motor has asymmetry. And if there is
significant value of harmonic amplitudes of 156–
195 Hz, that asymmetry is caused by unbalance.
a) b)
Fig. 4 Three-phase (a) and phase A (b) power spectra of
motor with rotor unbalance.
So, for detecting rotor unbalance, the following
rule should be true:
( ε > 0,
05)
∧ ( ε ≠ ε ≠ ε
p2
∧ ( P
avg А2
≠ P
avg B2
pA
≠ P
pB
avg C 2
) ∧ ( K
) ∧ ( K
t hh
harm(156-195)
> 0,
02)
> 0,
1)
∧ ( Kharm(196-
205) > 0,
45)
= 1.
In case of stator windings asymmetry and stator
windings short-circuits, there is significant harmonics
of double voltage frequency and little less then 4 f v
frequency (fig. 5 a, fig. 6, a). When damages are
worse, this harmonics grow. Low-frequency
harmonics (5–45 Hz) also grow, however its
frequency is constant. Main percent of high
harmonics for phases is in range of 96–105 Hz. Also
significant percent is from range of 196–205 Hz (fig.
5, b; fig. 6, b). When both kinds of damages are
caused, values of formulated indicators are almost
equal. Thus, if there is main harmonic with double
voltage frequency and significant harmonic of little
less then 4 f v frequency, and significant degradation
of formulated indicators, that there is windings
asymmetry or windings short-circuits.
a) b)
Fig. 5 Three-phase (a) and phase A (b) spectra of motor
with asymmetry of phase A.
pС
(
437
( K
( P
(( K
a) b)
Fig. 6 Three-phase (a) and phase A (b) spectra of motor
with stator winding short circuits.
So, if the following rule is correct:
> 0,
02)
∧ ( K ≠ K ≠ K
ε p2
npτ
(A) npτ
(B) npτ
(C)
∧ ( ε < 0,
98)
∧ ( ε
p
lq v
avg А2
> 0,
05)
∧ ( K
harm(196
≠ P
avg B2
- 205)
> K
pA
rec t
≠ P
≠ ε
< 0,
97)
∧
avg C 2
pB
harm(156-195)
≠ ε
) ∧ (( K
) ∨
pС
) ∧
harm(96-105)
)
> 0,
99)
∧
( Kharm(196-
205) ≈ Kharm(156-195)
)) = 1,
then there is either windings asymmetry or windings
short-circuits.
When rotor bar breaks, there is only low
frequency component in three-phase power spectra
(fig. 7, a). It grows when progresses defect.
Remaining indicators change negligibly and there is
no asymmetry of examined parameters, because
changing of rotor parameters appears indirect in
changing of stator parameters. Additional indicator
for identifying this defect is subharmonics of voltage
frequency in current spectra [3]. Thus, if there is low
frequency component of three-phase power signal,
also subharmonics of main voltage frequency
harmonic in current spectra, non-equal weighted
average quotients and almost optimal ε p , K rec t ,
then motor has rotor bar breaks.
a) b)
Fig. 7 Three-phase (a) and phase A (b) spectra of motor
with rotor winding bar break.
For detecting this defect, the following rule must
be correct:
( K ≠ K ≠ K ) ∧ ( ε ≈ ε ≈ ε )
npτ
(A)
∧ ( K
t hh
npτ
(B)
> 0,
02 ) ∧ ( P
npτ
(C)
avg А2
≠ P
pA
avg B2
≠ P
pB
avg C 2
) ∧
∧ ( Kharm(6
- 45) > 0,
8 ) = 1.
Thus, observing for variation of formulated
indicators, it is possible to make conclusion about
appearing of some kinds of defects or non-qualities
of asynchronous electric drive systems. Analyzing
values of some indicators it is possible to make
conclusion about current work mode allowability.
Also it is possible to prognosis remaining resource
analyzing non equal phase heating basis on "eight
degree" rule. When some defects are present for one
motor at the same time, percent of harmonics from
frequency ranges for each defect will be less than if it
pС

would be only one defect. Determination of defects
must be done by additional indicators, however if
defect is present, value of indicator Kharm(
N1
÷ N 2 )
must be greater than 0.1. Biggest value of high
harmonics indicator for one of frequency diapasons
imply about domination of this defect.
Theoretical conclusions and mathematical models
analysis results were vindicated by experimental
testing [23].
Analyzing experimental data of testing AD with
bad mounting supplying symmetrical and
asymmetrical voltage, the following conclusions were
made:
– when bad mounting, there is low frequent
component of three-phase power spectra (fig. 8).
This fact vindicates model analysis results;
Fig. 8 – Power consumption spectra when feeding
3-phase symmetrical power supply.
Fig. 10 – Voltage and current spectra for good motor.
Fig. 12 – Voltage and current spectra for motor with break
of three rotor winding bars.
Fig. 14 – Voltage and current spectra for motor with stator
winding short circuits (10% of phase A).
4. Conclusion
Additional indicators of energy conversion quality
were proposed. Analyzing existing and proposed
indicators, and also power consumption spectra,
rules for detecting most popular kinds of AD defects
were formulated.
Bibliography
[1] Котеленец Н.Ф., Кузнецов Н.Л. Испытания и
надежность электрических машин.
М.,“Высш.шк.”, 1988. – 232 с.
[2] Ермолин Н.П., Жерихин И.П. Надежность
электрических машин. М., “Энергия”, 1975. –
250 с.
438
– harmonic with frequency value of double
voltage frequency, generated by power supply
asymmetry (fig. 8, 9).
Analyzing experimental data for AD with stator
and rotor damages, it is possible to make following
conclusions:
– when rotor winding damages, there is harmonic
in three-phase power spectra (fig. 13) which conform
to rotation frequency (here - 24.194 Hz), and there is
subharmonics of voltage main harmonic frequency
in current signal (fig. 12);
– when stator windings short-circuits, there is
low-frequency harmonics in three-phase power
consumption spectra, like in modeling results
(fig. 14, 15).
Fig. 9 – Power consumption spectra when feeding 3-phase
unsymmetrical power supply.
Fig. 11 – Instantaneous power consumption spectra for
good motor.
Fig. 13 – Instantaneous power consumption spectra for
motor with break of three rotor winding bars.
1 . 10 4
1 .10 3
100
10
1 .10 3
0 200 400 600 800 1000 1200
0.1
0.01
Fig. 15 – Instantaneous power consumption spectra for
motor with stator winding short circuits (10% of phase A).
[3] Петухов В., Соколов В. Диагностика
состояния электродвигателей. Метод
спектрального анализа потребляемого тока.
// Новости электротехники №1(31) 2005
[4] B.Yazici, G.B.Kliman, W.J.Premerlani,
R.A.Koegl, A.Abdel-Malek, G.B.Robinson Online
statistical conditional monitoring and fault
diagnosis for motors with applications to rotor
bars and bearings // GE Research &
Development center, September 1997
[5] Aditya Korde B.E. On-line condition monitoring
of motors using electrical signature analysis //
presented at ‘Recent advances in condition-based
plant maintenance’ seminar 17-18 May 2002
[6] Internet resource:
http://www.vibration.ru/sredstva.shtml

[7] Мамчур Д.Г., Калінов А.П. Оцінка режимів
роботи асинхронних двигунів на основі
показників якості перетворення енергії //
Електромеханічні системи, методи
моделювання та оптимізації. Збірник
наукових праць VII ВНТК молодих учених і
спеціалістів. – Кременчук, КДПУ, 2009. – 418
с., - С. 244-249.
[8] Kalinov Andriy, Mamchur Dmitriy, Chumachova
Anna, Research Of The Asynchronous Motor’s
Observability For Estimation Operating
Conditions And Energy Efficiency // X
International PhD Workshop OWD’2008, рр.
357-362.
[9] Бессонов Л.А. Теоретические основы
электротехники. Электрические цепи:
Учебник. – М.: Гардарики, 2001. – 638 с.
[10] Чёрный А.П. Определение снижения ресурса
асинхронных двигателей по показателям
качества преобразования энергии // Збірник
праць Кіровоградського НТУ, 2004. – Вип.
15, – С. 160–168.
[11] Родькин Д.И., Чёрный А.П., Мартыненко В.А.
Обоснование критериев качества
преобразования энергии в
электромеханических системах // Проблемы
создания новых машин и технологий. Сб. научных
трудов КГПУ: Вып. 1. – Кременчуг,
2002. – С. 81–85.
[12] Родькин Д.И. Новая система показателей
качества использования электрической
энергии // Науковий вісник НГУ, 2004, –
№3. – С. 20–26.
[13] Чёрный А.П., Калинов А.П., Мамчур Д.Г.
Применение показателей качества
преобразования энергии для оценки
состояния и надёжности электомеханических
систем // Зб. наук. праць ДДТУ (техн. науки).
Тематичний випуск «Проблеми
автоматизованого електропривода. Теорія і
практика». – Дніпродзержинськ: ДДТУ, 2007.
– С. 519–523.
[14] Мамчур Д.Г., Калинов А.П. Развитие
показателей качества преобразования
энергии для диагностики технического
состояния асинхронных электродвигателей
// Вісник КДПУ ім. М. Остроградського,
Випуск 4/2008 (51). Частина 2. – С. 158–163.
[15] Моделювання електромеханічних систем:
Підручник / Чорний О.П., Луговой А.В.,
Родькін Д.Й., Сисюк Г.Ю., Садовой О.В. –
Кременчук, 2001. – 410 с.
[16] Мамчур Д.Г. Дослідження вібрацій механічної
частини електричних машин на
математичних моделях // Тези доповідей
п’ятої всеукр. НТК молод. вчен. і спец.
“Електромеханічні системи методи
моделювання та оптимізації”. Кременчук:
КДПУ, 2007. – С. 60–61.
[17] Калінов А.П., Мамчур Д.Г. Математичні
моделі для дослідження впливу
конструктивних несиметрій електричних
машин на їх електромагнітні параметри //
Вісник КДПУ. Наукові праці КДПУ. - Вип. 3
(44). – Ч.2 - Кременчук: КДПУ, 2007. – С.
150–154.
[18] Калинов А.П., Ухань Ж.И., Топчиенко Ю.А.
Исследование работы асинхронных
двигателей при повреждении обмоток ротора
// Тези диповідей шостої всеукр. НТК мол.
вчен. і спец. “Електромеханічні системи
методи моделювання та оптимізації”.
Кременчук: КДПУ, 2008. – С. 73–74.
[19] Петухов В., Соколов В. Диагностика
состояния электродвигателей. Метод
спектрального анализа потребляемого тока
// Новости электротехники. – № 1(31). 2005.
[20] Жежеленко И. В. Интергармоники сетевого
тока непосредственных преобразователей
частоты с искусственной коммутацией / И. В.
Жежеленко, Ю. Л. Саенко, Т. К. Бараненко
// Электрика. – 2005. – №5. – С. 16 – 22.
Библиогр.: с. 22.
[21] Калинов А.П., Мамчур Д.Г., Херардо Веласке
Ангуло. Отделение влияния
некачественности питающей сети на
электрические машины переменного тока в
задачах диагностики // Вісник НТУ «ХПІ»,
«Проблеми автоматизованого
електропривода. Теорія і практика» – Харків:
НТУ «ХПІ», 2008, № 30. – С. 559-563.
[22] Жежеленко И.В., Саенко Ю.Л. Вопросы
качества электроэнергии в электроустановках.
– Мариуполь: ПГТУ, 1996. – 173 с.
[23] Калінов А.П., Мамчур Д.Г., Браташ О.В.,
Ухань Ж.І., Простак О.І. Експериментальні
дослідження режимів роботи асинхронних
двигунів з неякісним кріпленням до основи та
з пошкодженнями обмоток статора і ротора
// Електромеханічні системи, методи
моделювання та оптимізації. Збірник
наукових праць VII ВНТК молодих учених і
спеціалістів. – Кременчук, КДПУ, 2009. – 418
с., - С. 250-253.
439
Authors:
Mamchur Dmytro,
Kremenchuk Mykhaylo
Ostrogradskiy State
Polytechnical University
ul. Pershotravneva, 20
39600, Kremenchuck,
UKRAINE
tel. (05366) 3-11-47
email: scenter@polytech.poltava.ua
Kalinov Andrii,
Kremenchuk Mykhaylo
Ostrogradskiy State
Polytechnical University
ul. Pershotravneva, 20
39600, Kremenchuck,
UKRAINE
tel. (05366) 3-11-47
email: scenter@polytech.poltava.ua